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Problem 16 Easy Difficulty

Use a computer algebra system to draw a direction field for the given differential equation. Ger a printout and sketch on it the solution curve that passes through (0,1). Then use the CAS to draw the solution curve and compare it with your sketch.
$ y' = x(y^2 - 4) $

Answer

Shown below is the graph of the direction field for $y^{\prime}=\cos (x+y)$
Purple curve in the graph below is the solution curve passing through $(0,1)$

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Video Transcript

Hello? Today we're looking at differential equations, and we've been given this equation. Why? Prime equals X times y squared minus four. And we've been asked to plot this. A solution curb that passes through the point 01 And so this is the little field for the directional field for this equation. Uh, you can search this up and to get this if you need that. Um, so remember to get all of these little lines right here. If you're plotting this by hand, you would plug in a point for X and y. So if we plug in the 0.0.1 you have X zero. Why is one and so you have white prime equals zero. And when you get a value zero, it's a straight line and we get a value of one. It's a 45 degree angle. So what's going on? Plot this solution curve that passes 3.1 So 01 is right here on our graph and and then we start drawing a line following the arrows, making sure we're not going over a any certain arrow. We get a curve like this on one side and on the other side we have a curve like this

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